Solve 1.69*4=x^2

$$1.69 \times 4 = x ^ { 2 }$$

Solve for x

$$x=2.6$$

$$x=-2.6$$

Steps Using Difference of Squares

Multiply 1.69 and 4 to get 6.76.

$$6.76=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=6.76$$

Subtract 6.76 from both sides.

$$x^{2}-6.76=0$$

Consider x^{2}-6.76. Rewrite x^{2}-6.76 as x^{2}-\left(\frac{13}{5}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-\frac{13}{5}\right)\left(x+\frac{13}{5}\right)=0$$

To find equation solutions, solve x-\frac{13}{5}=0 and x+\frac{13}{5}=0.

$$x=\frac{13}{5} x=-\frac{13}{5}$$

Steps by Finding Square Root

Multiply 1.69 and 4 to get 6.76.

$$6.76=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=6.76$$

Take the square root of both sides of the equation.

$$x=\frac{13}{5} x=-\frac{13}{5}$$

Steps Using the Quadratic Formula

Multiply 1.69 and 4 to get 6.76.

$$6.76=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=6.76$$

Subtract 6.76 from both sides.

$$x^{2}-6.76=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -6.76 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-6.76\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-6.76\right)}}{2}$$

Multiply -4 times -6.76.

$$x=\frac{0±\sqrt{27.04}}{2}$$

Take the square root of 27.04.

$$x=\frac{0±\frac{26}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{26}{5}}{2} when ± is plus.

$$x=\frac{13}{5}$$

Now solve the equation x=\frac{0±\frac{26}{5}}{2} when ± is minus.

$$x=-\frac{13}{5}$$

The equation is now solved.

$$x=\frac{13}{5} x=-\frac{13}{5}$$